# Factor Group and Torsion Group

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Heres my problem.

Consider the group <R,+> (reals under addition) and its normal subgroups Z (integers) and Q (rationals0. (These are normal because R is abelian,

of course.)

(i) Find an element of Q/Z of order 350.

(ii) Show that Q/Z is the torsion subgroup of R/Z. This problem is quite straightforward if you use the definitions and stay focussed; in

particular, pay attention to the definition of a rational number.

(iii) Show that R/Q is torsion free. Think carefully about the elements of R that are not in Q here.

https://brainmass.com/math/basic-algebra/factor-group-and-torsion-group-30949

#### Solution Summary

Factor Groups and Torsion Groups are investigated. The solution is detailed and well presented.

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